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%I #24 Oct 27 2024 10:56:51
%S 37,37,333667,9901,2906161,333667,10838689,99990001,440334654777631,
%T 2906161,1344628210313298373,999999000001,900900900900990990990991,
%U 10838689,4185502830133110721,9999999900000001,13168164561429877,440334654777631,3931123022305129377976519,39526741
%N a(n) is the greatest prime divisor of 10^(2*n)+10^n+1.
%C (10^(2*n)+10^n+1)^3 is palindrome.
%H Amiram Eldar, <a href="/A190839/b190839.txt">Table of n, a(n) for n = 1..158</a>
%H factordb, <a href="http://factordb.com/index.php?query=10^%282*n%29%2B10^n%2B1&use=n&n=1&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show">10^(2*n)+10^n+1</a>.
%F a(n) = A006530(A066138(n)). - _R. J. Mathar_, Oct 30 2015
%t f[n_]:=Max[Transpose[FactorInteger[10^(2n)+10^n+1]][[1]]]; Array[f,20] (* _Harvey P. Dale_, Jun 10 2011 *)
%o (PARI) u(n)=10^(2*n)+10^n+1; for(n=1,30,f=factor(u(n));print1(f[matsize(f)[1],1],", ")) \\ _Joerg Arndt_, May 27 2011
%Y Cf. A002780, A006530, A066138.
%K nonn,base
%O 1,1
%A _Vladimir Shevelev_, May 21 2011